1. Field of the Invention
This invention relates to electronic circuits, and more particularly, the design of power distribution systems.
2. Description of the Related Art
As computer systems advance, there is a continuous demand for systems which demand higher power at a relatively low voltage. Designing power distribution systems that can deliver a large amount of current at a low voltage is a significant challenge. Tight voltage tolerances (e.g. ±5%) are often times required to ensure the proper performance of silicon chips within a computer system. The lower operating voltages may result in much lower target impedance requirements. At the same time, the clock frequencies for microprocessors and other types of silicon chips is continually increasing, thereby resulting in a much wider frequency range for which target impedance requirements must be met.
Power distributions systems typically include at least one pair of planar conductors (e.g. a power plane and a ground plane), separated by a dielectric layer. A plurality of capacitors may be electrically connected in a parallel configuration between the planar conductors in order to provide a low impedance path for power distribution. Many power distribution system employ a plurality of ceramic capacitors mounted upon a printed circuit board (PCB). Such capacitors may be chosen based on their ability to meet target impedance requirements for a given frequency, and capacitors having different values may be chosen to meet the target impedance requirements over a wider frequency range.
Electrical characteristics of capacitors which must be considered when designing power distribution systems include capacitance, equivalent series resistance (ESR) and equivalent series inductance (ESL). These characteristics have a significant effect on the electrical response of a given capacitor over a frequency range. At lower frequencies, the impedance provided by a capacitor is dominated by its capacitance. Since capacitors include conductive elements, such as conductive plates and mounting pads or pins, there is an inductance (ESL) associated with them. This inductance dominates the impedance profile of a capacitor at higher frequencies. The point at which the inductive and capacitive reactances cancel each other out is known as the resonant frequency, and the impedance provided by the capacitor at this frequency is known as the ESR.
FIG. 1 illustrates the frequency response for a typical capacitor. At lower frequencies, the impedance decreases with frequency at a rate of approximated −20 dB/decade. At these frequencies, the impedance provided by the capacitor is dominated by capacitance, and may be calculated by the formula       Z    =          1              j        ⁢                                   ⁢        ωC              ,where Z is the impedance, C is the capacitance, and ω is the angular frequency. As frequency increases, the capacitor will eventually achieve a state of resonance, as the capacitive reactance will be offset by the inductive reactance. This resonant frequency may be calculated by the formula       F    =          1              2        ⁢        π        ⁢                  LC                      ,where F is the resonant frequency, L is the equivalent series inductance, and C is the capacitance. The impedance provided by a capacitor at its resonant frequency is the capacitor's ESR. At frequencies above the resonant frequency, the impedance provided by a capacitor may be dominated by its ESL. The impedance of the capacitor for frequencies greater than the resonant frequency may be calculated by the formulaZ=jωL,where Z is the impedance, L is the ESL, and ω is the angular frequency. In designing power distribution systems, a plurality of capacitors having different impedance profiles may be combined in order to achieve a target impedance over a wide frequency range.
Designing power distribution systems and determining the necessary decoupling capacitors often times includes modeling and simulation. The power distribution system, as well as the various circuitry to which power is to be provided, may be modeled and simulated so as to predict the performance of the power distribution system. FIG. 2 is a schematic of one embodiment of a traditional electrical model for a capacitor. The embodiment shown is a model of a capacitor based on a series RLC circuit. The model includes a resistor representing the capacitor's ESR value, a capacitor representing its capacitance value, and an inductor representing its ESL value. The model may be implemented as a SPICE model or other type of mathematical for simulation on a computer system.
The capacitor model of FIG. 2 may be useful for simulation at lower frequencies, but may be inadequate for higher frequencies. As previously stated, power distribution systems typically include a pair of planar conductors separated by a dielectric, which may act as a capacitor at lower frequencies. At higher frequencies, a pair of planar conductors may develop impedance resonances that are associated with the parallel plate geometry. These impedance peaks are sometimes referred to as anti-resonances, or parallel resonances. The traditional series RLC circuit model of a capacitor may be unable to correctly predict the frequency or frequencies at which anti-resonances occur.
FIG. 3 is a graph illustrating the simulated and measured performance of a capacitor mounted between two power planes over a range of frequencies, wherein the simulation is based on the traditional model of FIG. 2. Both the simulated and measured results were for a pair of conductive planes (i.e. a power plane and ground plane) having a single capacitor mounted electrically connected between the planes. The capacitor model used for the simulated results was the traditional RLC series circuit model. As can be seen from examining the graph, model-to-hardware correlation is good for the lower frequencies. However, the simulated results differ from the measured results significantly with respect to both the frequency and magnitude of the first anti-resonant peak. In this particular example, the simulated results predict an anti-resonant peak at a lower frequency and of significantly higher magnitude than that obtained by the measured results. Second and third anti-resonant peaks also differ between simulated and measured results. The second anti-resonant peak from the measured results occurs at a frequency close to that which is predicted by the simulated results. The third anti-resonant peak for the measured results occurs at a higher frequency and lower magnitude than predicted by the simulated results.
The higher operating speeds of the various silicon chips in computer systems (or other electronic systems) often times results in the need for higher clock frequencies on system boards. Accurate modeling is important in designing power distribution systems for these systems. As such, the traditional RLC series circuit model for capacitors is no longer adequate for determining the necessary decoupling capacitors for a power distribution system.